Semi-supervised Learning based on Distributionally Robust Optimization

We propose a novel method for semi-supervised learning (SSL) based on data-driven distributionally robust optimization (DRO) using optimal transport metrics. Our proposed method enhances generalization error by using the unlabeled data to restrict the support of the worst case distribution in our DRO formulation. We enable the implementation of our DRO formulation by proposing a stochastic gradient descent algorithm which allows to easily implement the training procedure. We demonstrate that our Semi-supervised DRO method is able to improve the generalization error over natural supervised procedures and state-of-the-art SSL estimators. Finally, we include a discussion on the large sample behavior of the optimal uncertainty region in the DRO formulation. Our discussion exposes important aspects such as the role of dimension reduction in SSL

Predictive control of systems with fast dynamics using computational reduction based on feedback control information

Predictive control is a method, which is suitable for control of linear discrete dynamical systems. However, control of systems with fast dynamics could be problematic using predictive control. The calculation of a predictivecontrol algorithm can exceed the sampling period. This situation occurs in case with higher prediction horizons and many constraints on variables in the predictive control. In this contribution, an improving of the classical approach is presented. The reduction of the computational time is performed using an analysis of steady states in the control. The presented approach is based on utilization of information from the feedback control. Then this information is applied in the control algorithm. Finally, the classical method is compared to the presented modification using the time analyses. © Springer International Publishing Switzerland 2015

A Polynomial Optimization Approach to Constant Rebalanced Portfolio Selection

We address the multi-period portfolio optimization problem with the constant rebalancing strategy. This problem is formulated as a polynomial optimization problem (POP) by using a mean-variance criterion. In order to solve the POPs of high degree, we develop a cutting-plane algorithm based on semidefinite programming. Our algorithm can solve problems that can not be handled by any of known polynomial optimization solvers.

Robust and accurate online pose estimation algorithm via efficient three‐dimensional collinearity model

In this study, the authors propose a robust and high accurate pose estimation algorithm to solve the perspective‐N‐point problem in real time. This algorithm does away with the distinction between coplanar and non‐coplanar point configurations, and provides a unified formulation for the configurations. Based on the inverse projection ray, an efficient collinearity model in object–space is proposed as the cost function. The principle depth and the relative depth of reference points are introduced to remove the residual error of the cost function and to improve the robustness and the accuracy of the authors pose estimation method. The authors solve the pose information and the depth of the points iteratively by minimising the cost function, and then reconstruct their coordinates in camera coordinate system. In the following, the optimal absolute orientation solution gives the relative pose information between the estimated three‐dimensional (3D) point set and the 3D mode point set. This procedure with the above two steps is repeated until the result converges. The experimental results on simulated and real data show that the superior performance of the proposed algorithm: its accuracy is higher than the state‐of‐the‐art algorithms, and has best anti‐noise property and least deviation by the influence of outlier among the tested algorithms

On the Handling of Continuous-Valued Attributes in Decision Tree Generation

We present a result applicable to classification learning algorithms that generate decision trees or rules using the information entropy minimization heuristic for discretizing continuous-valued attributes. The result serves to give a better understanding of the entropy measure, to point out that the behavior of the information entropy heuristic possesses desirable properties that justify its usage in a formal sense, and to improve the efficiency of evaluating continuous-valued attributes for cut value selection. Along with the formal proof, we present empirical results that demonstrate the theoretically expected reduction in evaluation effort for training data sets from real-world domains.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46964/1/10994_2004_Article_422458.pd

Continuization of Timed Petri Nets: From Performance Evaluation to Observation and Control

Abstract. State explosion is a fundamental problem in the analysis and synthesis of discrete event systems. Continuous Petri nets can be seen as a relaxation of discrete models allowing more efficient (in some cases polynomial time) analysis and synthesis algorithms. Nevertheless computational costs can be reduced at the expense of the analyzability of some properties. Even more, some net systems do not allow any kind of continuization. The present work first considers these aspects and some of the alternative formalisms usable for continuous relaxations of discrete systems. Particular emphasis is done later on the presentation of some results concerning performance evaluation, parametric design and marking (i.e., state) observation and control. Even if a significant amount of results are available today for continuous net systems, many essential issues are still not solved. A list of some of these are given in the introduction as an invitation to work on them.

On the Non-Existence of Optimal Solutions and the Occurrence of “Degeneracy” in the CANDECOMP/PARAFAC Model

The CANDECOMP/PARAFAC (CP) model decomposes a three-way array into a prespecified number of R factors and a residual array by minimizing the sum of squares of the latter. It is well known that an optimal solution for CP need not exist. We show that if an optimal CP solution does not exist, then any sequence of CP factors monotonically decreasing the CP criterion value to its infimum will exhibit the features of a so-called “degeneracy”. That is, the parameter matrices become nearly rank deficient and the Euclidean norm of some factors tends to infinity. We also show that the CP criterion function does attain its infimum if one of the parameter matrices is constrained to be column-wise orthonormal